Question

In an experiment with $10$ observations on $x$ the following results are available $\displaystyle \sum x^{2}=354$ and $\displaystyle \sum x=58$ . If one observation that was $8$ was found to be wrong and was replaced by the corrected value $10,$ then the corrected variance is

• A. $5$
• B. $3$
• C. $4$
• D. $6$

Answer 1

Answer: (B)

$\sum x^{2}=354, \sum x=58$
$\sum x^{\prime}=58-8+10=60$
$\sum x^{\prime 2}=354+100-64=390$
Variance $=\frac{\sum\left(x^{\prime}\right)^{2}}{10}-\left(\frac{\Sigma\left(x^{\prime}\right)}{10}\right)^{2}=\frac{390}{10}-\left(\frac{60}{10}\right)^{2}$
$=39-36$
$=3$